Wednesday, September 02, 2015

Blowing Up The Moon

Just started reading Neal Stephenson's Seveneves. The novel starts with a bang: specifically, the Moon blows up. No one quite knows how the Moon blew up: some speculate about a primordial black hole (but we know from Greg Bear's The Forge of God that that wouldn't do it) but in the main, people refer to some unknown 'Agency' as the moving force behind the event.

The main thing is not so much that the Moon has exploded into fragments orbiting their common centre of mass, it's what will happen next. I could hardly believe it, so naturally searched the Internet for the 'Science behind Seveneves'. And came across this.

"There are many different ways in which a reader can imagine the moon blowing up—imagery of the death star annihilating Alderaan comes to mind as the most culturally ubiquitous. But Stephenson quickly establishes the hard-SciFi slant of the novel. There are no fireworks, no loud booms—the opening chapters read like historical fiction for what would actually happen if the moon was fractured into (mostly) gravitationally bound chunks by some unknown force. Chiefly, people would freak out a little bit.

An ensemble cast of characters and their reactions span the opening chapters. A character obviously modeled after Neil deGrasse Tyson, Jerome Xavier Harris (or Doob for short), is rapidly recruited to run popular science damage control—essentially, doing exactly what I would imagine Neil deGrasse Tyson doing if such an event were to happen: media appearances and public lectures explaining that the still-gravitationally-bound moon posed no danger.

In some sense, this is naively true. A common physics brain teaser is to ask what would happen if our sun were replaced by a black hole of equal mass. Barring the joke answer of “everything would probably freeze to death”, nothing much would happen. The black-sun would still be in the same place, with the same mass, thus the orbit of the earth would remain unchanged. As it’s established in the early pages of Seveneves, whatever unknown force which fractured the moon didn't send it on a direct crash-course with the earth—it just imparted enough energy to fracture it into a handful of pieces—pieces which remain in a wildly chaotic orbit around each other, but still somewhat confined to the general vicinity of the moon.

Orbital mechanics problems are notoriously tricky to solve. The so-called three-body-problem was one of the earliest problems tackled once the tools of calculus were developed by Isaac Newton in the late 1600s (a prominent character in Stephenson’s own Baroque Cycle). The problem is almost entirely explained by its title: how will three (or more) celestial bodies evolve in the night sky if you know their starting positions and velocities? Mathematicians eventually proved that there is no general analytic solution to the three-body-problem, barring a handful of special cases. The difficulty arises in the sensitivity of the problem to its initial conditions. If you don’t know exactly where the objects are and exactly how fast they’re going, your estimate can be wildly off.

Because numerical integration is really the only way to actually solve orbital mechanics problems, it’s clearly important that the chosen integration scheme be error free. Tools like Runge-Kutta and Euler integration are good, but they have technical shortfalls—they don’t manifestly conserve quantities that we know should be conserved. This sort of error is more than enough to yield completely nonsense results when trying to predict where things might be going in the night sky.

So, in one of my favorite scenes, when Doob realizes that the wildly chaotic orbits of the moonchunks might not be so harmless, and could even result in an exponentially increasing number of colliding and breaking fragments of moonstuff, I imagine that he sprinted to the nearest python terminal and coded up a symplectic integrator—an algorithm which is particularly good at orbital mechanics simulations. Whatever simulations canon-Doob did run, they soon indicated that the earth had about 2 years before the remaining moonchunks would rapidly break apart, and bombard the earth in moon-asteroids for approximately 10,000 years. This kills the planet. And everything on it.

I thought this would be nice to visualize, so I coded up a symplectic integrator and tried to see if I could reproduce what Doob calls the “White Sky” (the rapid dissolution of the moon) and the “Hard Rain” (the bombardment of the earth with asteroids). I tried to conserve mass and volume of moonchunks when they break apart and use a nearly elastic scattering model. With extremely generous assumptions, and the setting of arbitrary constants to 1 where convenient, I get something like this:

This simulation was very nearly contrived to produce an explosion of chunks in the beginning, and should be taken with a tremendous grain of salt, but hopefully it will allow you to at least suspend disbelief for the doomsday premise of the novel. The actual number of chunks and the rate at which they appear is, unsurprisingly, fairly sensitive to the initial conditions of the simulation. If nothing else, this simulation illustrates Kessler Syndrome fairly clearly—the rapid creation of dangerous debris from uncontrolled, chaotic orbits in space."

So there you have it: Stephenson was right (and/or was well advised).

A few pages in and before the disaster manifests, two feisty females on the International Space Station are discussing family matters. In a beautifully sardonic moment, we discover that one of them refers to the other's mother as 'the Maternal Organism'. Their conversation continues, punctuated with references to the morg.

My WhatsApp message to my sister this evening: "How did you find the morg today?"